Good Sets

Given an integer \(n\geq2\), suppose that there are \(mn\) points on a circle. We paint the points in \(n\) different colours so that there are \(m\) points of each colour. Determine the least value of \(M\) with the following property: for each \(m\geq M\), given any such colouring of the \(mn\) points, there exists a set of \(n\) points that contains one point of each colour, and with no two adjacent.

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